www.nature.com/scientificreports OPEN Surface wave manipulation by plasmonic metasurface based on mode resonance Baoshan Guo We proposed a method to manipulate the surface waves with a deep subwavelength metasurface by applying resonators with interfering mode resonance. The simulation results demonstrate that a single deep subwavelength obstructed groove can efectively control the propagation of surface terahertz (THz) waves by a small step increase (< 1/20 λ) of the depth or a slight change of refractive index (Δn = 0.1). The surface waves transmitted and refected by the single groove can be controlled periodically by increasing the groove depth or refractive index with a high efciency owing to the mode resonance between surface spoof plasmonics modes and groove cavity modes. The generated circle resonance mode provides a new idea for the development of THz devices. Importantly, the transmitted or refected intensity of the surface wave is also enhanced by the Mode resonance. It is a simple and efective method to operate surface THz waves and manufacture more compact integrated optical devices in deep subwavelength scale. Te most important characteristic of plasmonics is to confne the electromagnetic (EM) energy and enhance the interaction between light and matter in the subwavelength range 1,2, which has been applied in a wide range of felds, such as the miniaturization of photonic circuits3,4, near-feld optics and microscopy5,6, biological sensors7,8, and photovoltaics9,10. At terahertz (THz) frequencies, various subwavelength metal structures based on spoof SPPs (SSPPs)11–13 have been developed to efciently control the properties of THz felds14–20. Based on this, a series of new THz devices with high performance have been developed and applied in diferent areas, such as THz sensors21–23, THz spectrum and imaging detection24–26, and THz communication27. One of the most repre- sentative devices is the one-dimensional THz metal grating waveguide, which has been designed and fabricated into diferent groove shapes, including rectangular, inclined rectangular, trapezoidal, V-shaped, serrated and meniscus grooves28–37. If the surface grating has gradient depth 38–42, gradient period43, and vertical or downward pyramid grooves44, it can realize the so-called "trapped rainbow" that has been proved to be a refection rather than a real EM wave trapping45,46. In addition to the groove shape of the grating, the surface EM wave can also be controlled by changing the local refractive index of the dielectric layer covering the metal grating, just as a new dielectric grating is formed above the metal grating47. In fact, the change of refractive index in a groove of the metal grating itself can also signifcantly change the transmission characteristics of the surface wave, which will be discussed below. Furthermore, detailed understanding of the physical mechanism underlying single-groove manipulation of EM waves still needs study whether there is a covered dielectric layer or not. In this paper, it is revealed that the controlling of surface EM waves can be achieved by simply changing the depth or refractive index of a single deep subwavelength groove in the metal grating, and detailed physical explanation is given. With the increase of the groove depth or refractive index, the surface wave propagation characteristics show obvious periodic changes, which is essentially caused by the mode resonance between the surface modes and the groove cavity modes, similar to the Fano resonance 47–50. Moreover, under the mode resonance, the grating surface will form high-intensity local standing waves, which can be applied to deep subwavelength resonators or spasers. Simulation and discussion Te metal grating (Fig. 1) has rectangular grooves with depth (d), width (w), and period (p). By simply adjust- ing the main parameters of depth (d), width (w), and period (p), it can be designed to propagate or deceler- ate EM waves of diferent frequencies, because the dispersion property of the grating is determined by theses parameters11,13,45. In addition, as previously mentioned, the refractive index (n) of the material flling in the grooves can also afect the propagation of the EM waves. To further investigate how to control the surface EM waves by the mode resonance between the grating and its single groove, a metal grating model (Fig. 1) is Laser Micro/Nano Fabrication Laboratory, School of Mechanical Engineering, Beijing Institute of Technology, Beijing 100081, China. email: [email protected] Scientifc Reports | (2021) 11:3313 | https://doi.org/10.1038/s41598-021-82948-0 1 Vol.:(0123456789) www.nature.com/scientificreports/ Figure 1. Schematic of metal grating showing width (w), period (p), depth (d), and refractive index (n) of the material flling in the single grey groove. Te surface waves propagate along the direction of the X axis as shown by the black arrow. Figure 2. Intensity of surface waves at 3.75 THz before (a) and afer (b) the single grey groove of varying depth (Δd) and refractive index (Δn). established and simulated by the fnite diference time domain (FDTD) method. A special groove with gradual changes in refractive index (n) is marked in grey in Fig. 1. Te grating model with a uniform cell of ∆x = ∆z = 1 μm is treated as a perfect conductor (PEC) during the FDTD simulation, and surrounded by a perfectly matched absorption layer. Te depth and refractive index of the flling media of the single grey groove are the main param- eters to control the propagation of surface waves. At 1000 μm to the lef of the single grey groove, a p-polarized (Hy, Ex, Ez) THz source is introduced in the form of end fre excitation and used to excite the surface THz waves to propagate from lef to right as shown by the black arrow in Fig. 1. Te cutof frequency of a metal grating with period of 20 μm, width of 10 μm and depth of 10 μm is lower than 4.6 THz45. Hence, a source of 3.75 THz is used to excite the propagating surface wave, which propagates smoothly along the grating until it encounters the special grey groove (as shown in Fig. 1). In the simulation process, we only change the depth and refractive index of the single grey groove. Te surface wave intensities before and afer the single groove are recorded by two monitors, respectively, so as to analyze the surface wave intensities refected and transmitted by the single groove. According to the FDTD simulation results (Fig. 2), the surface wave intensities before (refection) and afer (transmission) the single groove are all changed periodically with the increase of groove depth (Δd) or refractive index (Δn). Te intensity of electric feld at localized points could be larger than “1” because of the joint contribution of mode resonance between plasmonic surface mode and groove cavity mode, and the interference between refection surface wave and incident wave. For a grating working as a normal waveguide, the monitored intensity values at the refection and transmission points are almost same and far below “1” as shown in Fig. 3. For example, at the zero point of Fig. 3a, Δn = 0, Δd = 0 μm, the grey groove is exactly same with other grooves, and the grating becomes a normal grating. Terefore, the transmission and refection intensity are all approximately equal to “0.4”, which is a base intensity of the surface wave. When the refection gradually increases and the transmission gradually weakens, the measured refection intensity starts to be greater than “0.4”, while the transmission intensity is gradually less than “0.4”. Hence, the refection and transmission intensity value are very diferent. It is also the reason why the scale bar value in Fig. 2a, b are dif- ferent. Te refection intensity defned here is changing on the base intensity of “0.4” as shown in Fig. 2a. For the single groove of Δn = 0 (n = 1) (Fig. 3a), the changing period of the surface wave intensity with the depth is approximately 30 μm. And the intensity peak shows a clear asymmetry shape, which is similar to the Fano resonance between the grating surface modes and groove cavity modes. When Δn = 0.5 (n = 1.5) (Fig. 3c), the changing period with depth is decreased to 20 μm (equals to 30 μm / 1.5), which means the efective wave- length is decreased corresponding to the increase of refractive index. For Δd = 0 μm (Fig. 3b), the refection of the surface wave is sharply increased frst with the increase of Δn, and is decreased slowly afer the peak (Δn ≈ Scientifc Reports | (2021) 11:3313 | https://doi.org/10.1038/s41598-021-82948-0 2 Vol:.(1234567890) www.nature.com/scientificreports/ Figure 3. Intensity of surface waves before (black solid line) and afer (red dashed line) the single grey groove of varying depth, Δn = 0 (a), Δn = 0.5 (c); and various refractive indices, Δd = 0 μm (b), Δd = 40 μm (d). 0.4) (black line in Fig. 3b). Te transmission intensity (black line in Fig. 3b) of the single groove shows a trend opposite to the refection intensity (red dashed line in Fig. 3b). However, there is no obvious periodicity because the single groove is not deep enough to form obvious mode resonance. When the depth of the single groove is increased to 50 μm (Δd = 40 μm) (Fig. 3d), a serials of strong periodical mode resonance are generated with the increase of Δn. Utilizing the sharp asymmetry property of the Fano resonance, we can control the surface waves with high sensitivity and efciency. As an example, two points marked in Fig. 3a and two points marked in Fig. 3d are chosen, respectively, to demonstrate the ability of surface wave manipulation. Te two points marked in Fig.